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Simplify the expression to a polynomial in standard form:

(4x^2+x-1)(-3x^2-3x-3)(4x2+x−1)(−3x2−3x−3)

User WSBT
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1 Answer

7 votes

Answer:


(144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2)

Explanation:

To better understand the question we need to properly format the expression


(4x^2+x-1)(-3x^2-3x-3)(4x^2+x-1)(-3x^2-3x-3)

as we can see we have three brackets, we can proceed by first opening the first two brackets, we have.


(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\

we then continue by collecting like terms


=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)

we then solve for the remaining two brackets


(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\

we then continue by collecting like terms


=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)

from the two brackets we obtained
(-12x^4-15x^3-12x^2+3) each, we now have to multiply both terms together and solve we have


(-12x^4-15x^3-12x^2+3)(-12x^4-15x^3-12x^2+3)\\=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\

collecting and summing all like terms we have


=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\=144x^8+180x^7+180x^7+144x^6+255x^6+180x^5+180x^5-36x^4+144x^4-36x^4-45x^3-45x^3-36x^2-36x^2\\\\\=144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2

User Postgresnewbie
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